This invention relates to an electronic musical instrument of the digital type.
A harmonic synthesis type electronic musical instrument disclosed in U.S. Pat. No. 3,809,786 issued on May 4, 1974 shows a typical digital electronic musical instrument. This harmonic synthesis type electronic musical instrument is constructed to calculate respective harmonic components which constitute a musical tone, to multiply calculated harmonic components with corresponding amplitude coefficients, and then to synthesize the products to form a musical tone. However, when it is desired to synthesize a musical tone containing a great number of harmonic components, it is necessary to increase the number of the calculating time slots.
An improved electronic musical instrument capable of producing a musical tone containing many harmonic components without increasing the calculation speed is disclosed in U.S. Pat. No. 4,135,422 dated Jan. 23, 1979.
According to this patent, a musical tone is formed by operating the following equations: ##EQU1## where f(x) and f(y) represent functions containing time variables, and n any interger. If f(x) and f(y) in equations (1) and (2) are made to be f(x)=f(y)=.omega.t (angular frequency information) a buzz wave having a spectral envelope or distribution in which the amplitudes of the harmonic components are flat as shown by the waveform shown in FIG. 1A. When a coefficient term sin {.alpha.+(k-1).beta.} is added to equation (1) and calculated according to the following equation (3) it is possible to produce a musical tone signal having a frequency characteristic as if the signal were passed through a filter, as shown by FIG. 1B. ##EQU2##
As can be noted from equation (3), according to the electronic musical instrument disclosed in this U.S. Pat. the coefficient term necessary to produce a desired musical tone is given as a certain type of a frequency function.